Best idea would be to boil all 6 gallons, but not everyone can do that, in this case if you feel like you must use ice in the wort, which is. It necessary, ice bath or immerison cooler is just fine, I would say make sure it is clean like you say, and maybe also equally importantly make sure it tastes clean or has no taste at all, some ice taste disgusting to me, gives whatever I put it in a nasty off flavor.